Single-core and multi-core optical fibers are used in a variety of applications. In a single-core optical fiber, a single light-guiding core is contained within reflective cladding material. A multi-core optical fiber includes a plurality of such cores. Strain sensors such as Fiber Bragg Gratings (FBGs) may be attached to or embedded within the fiber along the fiber's length. FBGs may be formed by laser-inscribing, writing, or otherwise embedding a periodic variation of refractive index into the cores of the optical fiber. This effectively creates an in-line optical filter designed to block particular wavelengths of light transmitted through or along the core. Alternatively, Rayleigh scatter detectors can be used to detect elastic light scatter occurring within a given core at specific axial locations of the optical fiber. Using these and/or other strain sensors, the bending geometry of the optical fiber can be calculated. The calculated geometric data may be used in various ways to approximate the shape of an object to which the cable is attached.
Strain information from axially co-located strain sensors can be used to estimate the bending at each co-located sensor location along the fiber. Common methods for accomplishing this exist, including, those outlined by S. Klute et al. in “Fiber Optic Shape Sensing & Distributed Strain Measurements on a Morphing Chevron”, 44th American Institute of Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting & Exhibit, #AIAA 2006-624, Jan. 9-12, 2006, Reno, Nev. Such methods are highly dependent on the accuracy of successive strain measurements used to calculate the cable's bending parameters at discrete segments of the cable.
When a multi-core cable in particular is subjected to bending, the strain in each core depends on the curvature and direction of the bend, as well as on the arrangement of the various constituent cores within the cable in relation to the bending direction. In accordance with linear elastic tube theory, a light-guiding core positioned on the inside of a bend experiences a stress, i.e., a negative strain, while a core positioned on the outside of the bend experiences a positive strain. The amount of strain is proportional to the bend radius and to the position of each core relative to the center of the bend curve. Therefore, multi-core fibers can have additional utility in comparison to single core fibers when used for structural shape sensing and end effecter tracking.
Conventional fiber optic shape sensing approaches initialize and calibrate the sensors while the fiber is straight, i.e., when the fiber initially has zero curvature and zero strain. U.S. Pat. No. 7,813,599 to Moore (hereinafter Moore '599), which is hereby incorporated by reference in its entirety, is one such approach. However, in practical applications it may be relatively difficult to maintain a known core orientation, and thus the angular core orientation is not always known. Using conventional methods, the calibration of strain sensors while the fiber is in an arbitrary initial shape, which may or may not be straight, may introduce a bias error that can lead to a substantial error in shape measurement.
Additionally, conventional shape sensing approaches do not adequately account for the effects of common extrinsic forces on the fiber such as twisting and/or stretching. Extrinsic axial loading may be introduced into the fiber through attachment mechanisms such as adhesives or tape, by general handling of the fiber as in a catheter application, or by friction inside of a sheathing which may house the fiber in a given application. Such extrinsic loading can cause shape measurement errors to occur in prior art approaches for determining the shape and/or position of a multi-core fiber.